Since a multi-object shape contains the continuous graphics and the discontinuous graphics, the representation of the multi-object shape with traditional methods causes Gibbs phenomenon. For example, Fourier transform and continuous wavelet transform cannot exactly represent multi-object shape by finite terms because they have strong continuity. Hence, they are not suitable for representation of multi-object shape. As multi-object image retrieval consumes substantial computer resources, new methods and apparatus that assist in advancing technological needs and industrial applications in effective computation for reconstruction of multi-image shape by finite terms are desirable.